Question

A highway department executive claims that the number of fatal accidents which occur in her state does not vary from month to month. The results of a study of 162 fatal accidents were recorded. Is there enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month?

Month Fatal Accidents Jan-19 Feb-8 Mar-21 Apr-13 May-10 Jun-18 Jul-10 Aug-14 Sept-13 Oct-8 Nov-10 Dec-18.

Step 1 of 10: State the null and alternative hypothesis.

Step 2 of 10: What does the null hypothesis indicate about the proportions of fatal accidents during each month?

Step 3 of 10: State the null and alternative hypothesis in terms of the expected proportions for each category.

Step 4 of 10: Find the expected value for the number of fatal accidents that occurred in January. Round your answer to two decimal places.

Step 5 of 10: Find the expected value for the number of fatal accidents that occurred in April. Round your answer to two decimal places.

Step 6 of 10: Find the value of the test statistic. Round your answer to three decimal places.

Step 7 of 10: Find the degrees of freedom associated with the test statistic for this problem.

Step 8 of 10: Find the critical value of the test at the 0.1 level of significance. Round your answer to three decimal places.

Step 9 of 10: Make the decision to reject or fail to reject the null hypothesis at the 0.1 level of significance.

Step 10 of 10: State the conclusion of the hypothesis test at the 0.1 level of significance.

Answer 1

Answer:

H0: the number of fatal accidents which occur in her state does not vary from month to month

H1: Atleast one of the month has different number of fatal accidents

Under H0, the expected number of fatal accident in each month is E =(19+8+21+13+10+18+10+14+13+8+10+18)/12

= 162/12

=13.5

The calculations for Chi square test statistic is

Month	O	E	(O-E)^2/E
Jan	19	13.5	2.2407
Feb	8	13.5	2.2407
Mar	21	13.5	4.1666
Apr	13	13.5	0.0185
May	10	13.5	0.9074
Jun	18	13.5	1.5
Jul	10	13.5	0.9074
Aug	14	13.5	0.0185
Sep	13	13.5	0.0185
Oct	8	13.5	2.2407
Nov	10	13.5	0.9074
Dec	18	13.5	1.5
Total	162		16.666

The test statistic is

= 16.666

df = n-1= 11

Signiifcance level = 0.1

At 5% Significance level, the critical value of Chi square is 17.275

Since chi square calculated is less than chi square tabulated, Fail to Reject the null hypothesis

Hence, there is not  enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month.

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